Moment of force

The way that I can understand how torque works is to say that the greater distance from the rotation axis that you apply your force, the greater power you are delivering to your object - since the farther you are away from the rotational centre the faster something is moving on your rotating object.
But the way my book derives the relationship
(1) Ʃτ = Iα
is kind of mysterious to me, as I don't see where my interpretation shows up during the steps.
They say let F be a force applied to the object. Every i'th particle will experience an acceleration such, that the angular velocity is the same for our rigid body. We thus have:
Fi = mi * a = mi * r * α
And multiplying with r yields:
τi = mi * r^2 * α
And summing over all torques gives us (1) - i.e. the rotational analogue of Newtons 2nd law. All there is left to show is then that the internal torques add to zero, but that's simple. I just don't see where the energy interpretation appears in this derivation - can someone open my eyes? :)